$\begin{array}{l}{\text { In each game played one is equally likely to either win or lose 1. Let } S \text { be your }} \\ {\text { cumulative winnings if you use the strategy that quits playing if you win the first }} \\ {\text { game, and plays two more games and then quits if you lose the first game. }} \\ {\text { (a) Use Wald's equation to determine } E[S] \text { . }} \end{array}$
Let $X_i$ be the amount won in game $i$. $$E[S] =E\bigg[\sum_{i=1}^N X_i\bigg]$$ Applying Walds theorem, $$=E[N]E[X]$$ And since this is a fair game where the player starts with 0 dollars, we know that $E[X]=0$. So, $E[S]=0$
Is this correct?